The idea that there is an evolutionary connection between dwarf galaxies of different morphogical types is not a new one, with many contributions pro and contra in the literature. During the last couple of years, it has become increasingly clear that the environment plays a crucial role in shaping dwarf galaxies and in driving their evolution. Theoretically, there are many ways of converting gaseous, star-forming late-type dwarfs into gas-poor early-type dwarfs. Hydrodynamical simulations show that ram-pressure stripping by the hot intra-cluster gas could completely remove the ISM of a low-mass dwarf elliptical (dE) or Blue Compact Dwarf (BCD) within a few 100 Myrs (Mori & Burkert, 2000, ApJ, 538, 559). The frequent high-speed interactions with giant cluster-members to which a small late-type disk galaxy (Sc-Sd) is subjected can transform it into a spheroidal dE-like object (Moore et al., 1996, Nature, 379, 613). This galaxy harassment process induces a dramatic morphological evolution in a time-span of about 3 Gyr. The fading model conjectures that star-forming dwarf galaxies will fade and reach an end-state similar to present-day dEs after they have used up their gas supply and star-formation has ended (Marlowe et al., 1999, ApJ, 522, 183). Interactions may speed up the gas-depletion process, explaining both the abundance of dEs and the paucity of BCDs in high-density environments. In this contribution, we report on new evidence for this idea, which was assembled by us in the course of an ESO-VLT Large Program on the kinematics and dynamics of dEs and from subsequent multi-wavelength follow-up observations with the VLT and with the ATCA radio telescope. Some of the arguments Pro a link between the different dwarfs are: (1) dEs, BCDs, and dwarf irregulars (dis) all have exponentially declining surface-brightness profiles. (2) dEs and dis follow a common sequence in an MB versus 〈μ〉e diagram (Ferguson & Binggeli, 1994, A&ARv, 6, 67). (3) Non-nucleated dEs and dis have similar spatial distributions inside clusters. (4) dEs and late-type dwarfs occupy the same locus within the Fundamental Plane (De Rijcke et al., 2005, A&A, in press). We now review the existing arguments Contra this link and discuss how our observations shed a new light on this problem. (1) dEs are found predominantly in clusters while BCDs are remarkably scarce in these high-density environments (Drinkwater et al., 2001, MNRAS, 326, 1076). This suggests that the star-formation rate and the gas content of galaxies is a function of environment. This is supported by our observations of dEs in the Fornax Cluster that contain ionised (Michielsen et al., 2004, MNRAS, 353, 1293) and neutral (Buyle et al., 2005, MNRAS, tmp, 469) gas. These gas-rich dEs all reside in the low-density outskirts of the cluster. (2) The gas in BCDs is rotationally supported (Van Zee et al., 2001, AJ, 122, 121; Östlin et al., 2001, A&A, 374, 800) while the stellar kinematics show that most dEs rotate slowly (Ferguson & Bingelli, 1994). However, we now know that there is also a significant population of fast-rotating dEs (De Rijcke et al., 2001, ApJL, 559, 21; Simien & Prugniel, 2002, A&A, 384, 371; De Rijcke et al., 2003, A&A, 400, 119) and we know dEs to contain HI gas with ordered rotation (Buyle et al., 2005). Either these dEs are simply faded BCDs/dIs or they stem from harassed late-type dwarf disks (Mastropietro et al., 2004, astro-ph/0411648). Moreover, we have fitted dynamical models to the observed kinematics of a sample of dEs. From these dynamical models one can infer the circular velocity curve (for elliptical galaxies, this is the only way to obtain the rotation curve). We are now for the first time able to directly compare the Tully-Fisher and vc versus a relations of dEs and dIs. (3) BCDs and dis contain relatively large amounts of both neutral and ionised gas whereas dEs were thought to possess much less of an ISM. However, we recently discovered dEs that contain neutral and ionised gas and may actively be forming stars, albeit at a very leisurely pace (Michielsen et al., 2004, MNRAS, 353, 1293; Buyle et al., 2005). Hence, thanks to the rapid progress that has been made in the last few years, both theoretically and observationally, the possibility that dwarf galaxies of different morphological types share evolutionary links is now much better supported. Also, it has become very clear that the ram-pressure and the gravitational interactions that dwarf galaxies undergo in a dense cluster environment have a profound influence on their evolution and that these processes can transform dwarf galaxies from one type into another within a time-span of a few gigayears.